The illogical numbers are numbers that seem to defy logic as we currently know it due to the strange way they are produced. The illogical numbers are similar to the natural numbers with the only difference being that they can be in any order you like. So for example the sequence 1,2,3 can also be written as 3,2,1 with no consequences whatsoever. One of the weird things about these illogical numbers is that they can be used to solve any algebraic problem such as x^2+1=0. Normally this would equal i the solution to the square root of negative 1 but in the illogical number system x can equal any number and still produce out 0. For example lets say we make x=5 and plug it into the formula 5^2+1=0 in normal mathematics of which everyone is familiar 5^2+1 would equal 26 but in the illogical number system it can equal whatever you like. If you think this is strange you should see what happens when you try to add two numbers together in this very crazy and illogical system of numbers. Lets take the simplistic example of 1+1 a classic example of a basic addition quite possibly the simplest expression of all time in normal mathematics this would equal 2 but in the illogical number system it can equal itself! In fact not only could it equal itself it could even equal something that isn't a number like the letter a. This highly flexible variable system of numbers allows for an infinite number of solutions to one equation using only 1 variable. Subtraction of these highly flexible numerical variables can not only reach numbers well below 0 but also below absolute infinity or trans-infinity an illogical concept that go's against all concepts of real world logic. trans infinity is infinity that exists in negative and positive absolute infinity at the same time this makes it infinitely small and infinitely large at the same time ! In the highly flexible variable system of numbers division by zero is possible as the answer can be made to equal any variable you want so for example 1/0 could equal 7. It is impossible to produce exact answers to solutions in this system of mathematics as the answer can be whatever you like. Not only are numbers affected but so ever geometric figures like regular polygons. Take a triangle the most stable polygon known to man in the normal world or the one we currently live on the angles must exactly equal 180 but in the highly flexible variable system of mathematics the angles can add up to whatever you like including but not limited to trans infinity. The next regular polygon that behaves slightly differently to its real world counterpart is the quadrilateral or bi dimension 4 gon. The quadrilateral in the real world has exactly 4 sides but in the highly flexible variable system of mathematics this isn't the case as their can be any number of sides depending on the circumstances. So for example a quadrilateral can have negative 4 sides and positive 4 angles where the sum of its angles adds up to square root of 4/4.4. This ability for the angles and sides of polygons to act as highly flexible variables makes it possible for them to perfectly tessellate the euclidean plane. Before we go to discover more about this remarkable system of mathematics that uses the concept of variables to quite literally do the unexpected we need to list as many regular polygons as we can if this seems odd to you at first I will explain afterwards. Triangle,quadrilateral,pentagon,hexagon,heptagon,octagon,nonagon,decagon,undecagon,dodecagon,tridecagon,tetradecagon,pentadecagon,hexadecagon,heptadecagon,octadecagon,enneadecagon,icosagon,icosikaihenagon,icosikaidigon,icosikaitrigon,icosikaitetragon,icosikaipentagon,icosikaihexagon,icosikaiheptagon,icosikaioctagon,icosikaienneagon,triacontagon. Here is the list of all polygons from the 3 gon to the 30 gon. The limit of this list of polygons will go into the realm of trans infinite polygons and complex polygons or polygons with a complex number of sides. Beyond this realm of 2 dimensional objects or abstract 2 gons in standard euclidean geometry at the level of the plane is the 3rd dimension. In the highly flexible variable system of mathematics objects that exist in the 3rd dimension can exhibit an infinite number of properties such as the ability to literally morph into any other 3d solid. So for example what appears to be a cube could actually be a sphere. 4d polytopes are even crazier as they exhibit such properties as being able to exhibit in negative and absolute dimensions at the same time. Like normal mathematics a polytope can exist in an infinite number of dimensions with the only difference being that in the system of mathematics we are talking about they can exist in all dimensions at the same time. Now lets get back to numbers and more specifically large numbers. Although this system of mathematics is very useful due to it allowing an infinite number of solutions to any problem in mathematics it still requires some rules or restrictions that stop it from getting out of hand. Lets say that you define the expression 10^5 to be equal to 10^10^10^10^10^5^5^5^5^5 in the real world this answer is flat out wrong but in the highly flexible variable system of mathematics it is write as you have said that 10^5 is equal to 10^10^10^10^10^5^5^5^5^5. By saying that the former is equal to the latter by definition it must be true regardless of what logic says as this system of mathematics follows its own logic. This system of logic can even extend to such things as probability. Lets start with a basic example with the classic example of the coin toss where it can either land on heads or tails. This analogy would be true in the context of the real world but in the world of highly flexible variables this isn't the case as the coin can exist in 2 states at the same time or even 0 states. This is called Schrodingers coin a thought experiment based on Schrodingers cat that states a coin tossed in the air has equal probability of landing on heads or tails until it lands. In the real world the outcome can't be decided but in the world of highly flexible variables the rules are slightly different as you can decide what the outcome will be making it more of a game of decision than a game of chance. This can extend to any game of chance whatsoever from rolling die to poker. Due to the highly flexible variables system of mathematics ability to bypass all known laws of chance it allows for any outcome to happen. This system of logic or unlogic as one might call it as it exists outside of the bounds of everyday logic extends beyond mathematics and into linguistics. Take a word like cat and say that it equals dog so that you get the expression cat=dog. Like numbers words can act as variables with an infinite number of solutions being produced from them. Words don't just act as highly flexible variables in this system of logic they can also have different meanings depending on what meaning you decide to give them. So for example lets say that we define a carrot to be a large tree containing large traces of mercury. This definition might seem flat out wrong but in the highly flexible variable system of logic this definition is correct and so is the definition that a carrot is not a carrot. By this definition of definitions it means that all definitions are correct no matter how crazy they may seem. Here is a list of very large numbers constructed using the highly flexible variable system of mathematics. Let 1=10^100^1000^10000 and by definition let 10=99999999999999999999999999999^99999999999999999999999999. We take this brilliant notion of making numbers equal whatever we want and apply the laws of highly flexible variable mathematics to it so as to produce a number of infinite complexity. Now lets say that we decide that the answer to this should and must be equal to 50!50 or 50 followed by 50 factorial signs. This comes to answer of 49 PT (1.947985576371 × 10^66) a relatively small number that has no real significance to anyone. We can do even more ridiculous things such as saying that 1+1= {500,500 (500) 500} in BEAF. This answer is correct in the sense that all numbers in this system of logic of which I am describing are variables with an endless number of solutions. Other things that have changed quite differently in this system of weird logic or illogical logic as one might call it are the very laws that hold the universe we live in together. This means that anything that is possible will happen if one chooses to let it happen so for that matter if one decides that they don't exist they don't exist. Everything in this highly flexible variable system of logic is based on choice rather than what makes sense. By this I mean that if someone decides that a=b then a definitely does equal b but at the same time a equals a+i or a=fish-salad. There are a few rules that govern this system of logic that prevents it from doing slightly more crazy things than it is supposed to. Rule 1: there can't be more than 551 solutions to an equation if the specified value of the variables is defined to sum up to the square root of -pi. Rule 2: rule 1 is false as their are an infinite number of solutions to all equations with just 1 variable. Rule 3: all solutions are correct in the sense that there are no wrong answers by the laws of multi variable solutions. Rule 4: it is likely that 96.54% of rabbits don't understand anything written here. Rule 5: rule 4 makes no sense. Rule 6: All attempts to come up with a true definition of the highly flexible variable system of logic will be in vain as there is no such thing as a pure definition. Rule 7: All attempts to understand rule 6 will be in vain. Rule 8: the chances of a game of chance going wrong according to the rules described previously are exactly pi+e/6:43.2. So there you have it the 8 rules of the highly flexible variable system of logic a system of logic that allows for an infinite number of solutions using a finite number of variables. The next thing that we must cover on this highly illogical journey is a very interesting number that displays one of the laws of highly flexible variables called the lynz. Before we talk about the lynz we need to talk about what this rule is,the rule states that any number defined to grow over time will do so regardless of if you say it wont. If you don't know the story of the lynz well here it is,on February the 26th 1998 a chemistry teacher gave lines to one of his pupils named Adam Clarkson. The lines read "I must always tuck my shirt in whilst participating in a chemistry lesson." Now the catch is that he had to do 100 by the 27th or they would double making the line number of lines due on the 28th 200. Too illustrate this idea here is a list of the appropriate dates and their values. 27/2/98=100 28/2/98=200 1/3/98=400 2/3/98=800 3/3/98=1600 4/3/98=3200 5/3/98=6400 6/3/98=12800 7/3/98=25600 8/3/98=51200 9/3/98=102400 10/3/98=204800 11/3/98=409600 12/3/98=819200 13/3/98=1638400 14/3/98=3276800 Lets skin forward a bit by 1 week. By the 21/3/98 the number of lines due will be 419430400. By the 28/3/98 the number of lines due will be equal to 53687091200. One week after that or the 4/4/98 the number of lines due will be equal to 6871947673600. One week after that the number of lines due will be equal to 8.796093022208*10^14 or just over 8 trillion. One week after that or the 18/4/98 the number of lines will be equal to 1.125899906843 × 10^17. As you can see the lynz is growing in a very linear but exponential way. Now to link the idea of the lynz back to the highly flexible variable system of logic. In the highly flexible variable system of logic we are allowed to define dynamic numbers like the lynz if the solution so requires it. What this rule is telling us is that if a solution requires a certain answer then you must use that answer. This system of logic may seem strange and unforgiving as it is as far out to logic as logic is to non logic. But if we think carefully about it the notion of highly flexible variables becomes pretty easy to understand. The next part of this fascinating system of logic that we will discover is the notion of totally ordered randomness or tor for short. Totally ordered randomness refers to systems that appear to be random like people in crowd but actually follow an ordered pattern. The law of totally ordered randomness takes the rules of Ramsey theorem to another level as not only will patterns emerge with a large enough specimen but patterns must exist in very small specimens as well. Another thing of interest to the study of highly flexible variables are fractals geometric patterns that are the same at every level,by this I mean that no matter how far you zoom into them you will always get a certain pattern/patterns. Fractals are of interest to those who study the highly flexible variable system of logic as they appear to be highly complex patterns but are in fact very ordered patterns meaning that they follow the law of totally ordered randomness. This law of totally ordered randomness states that nothing that appears to be random is actually random in the sense that their must exist some connection between sub parts of the system. Before we move on I want to point one thing out this system of logic may appear to be illogical but it actually follows a very simple set of rules. These laws can allow for the logical to become illogical if that doesn't make sense to you I will explain. Lets say that someone says to you that 2+2=84 now being a highly logical creature you quite rightly say this is wrong the only problem is if the person who told you that 2+2=84 was using numbers as highly flexible variables then this answer would indeed be correct. Too finnish off here is a list of solutions to the equation 1+1=x x=1 x=554 x=x+sqrt(i) x=pi-e+i^x-k x=65.6*10^665 x=554.1+56e/6.6-pi x=-1/12 So there you are have it an introduction to the highly flexible variable system of logic.